IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2781-d881365.html
   My bibliography  Save this article

A Game Theory Proof of Optimal Colorings Resilience to Strong Deviations

Author

Listed:
  • Dario Madeo

    (Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100 Siena, Italy)

  • Chiara Mocenni

    (Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100 Siena, Italy)

  • Giulia Palma

    (Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100 Siena, Italy)

  • Simone Rinaldi

    (Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, 53100 Siena, Italy)

Abstract

This paper provides a formal proof of the conjecture stating that optimal colorings in max k -cut games over unweighted and undirected graphs do not allow the formation of any strongly divergent coalition, i.e., a subset of nodes able to increase their own payoffs simultaneously. The result is obtained by means of a new method grounded on game theory, which consists in splitting the nodes of the graph into three subsets: the coalition itself, the coalition boundary and the nodes without relationship with the coalition. Moreover, we find additional results concerning the properties of optimal colorings.

Suggested Citation

  • Dario Madeo & Chiara Mocenni & Giulia Palma & Simone Rinaldi, 2022. "A Game Theory Proof of Optimal Colorings Resilience to Strong Deviations," Mathematics, MDPI, vol. 10(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2781-:d:881365
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2781/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2781/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2781-:d:881365. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.